The influence of the gluing process on the birefringence of surface-glued FBGs that were inscribed in highly birefringence (HiBi) optical fibers of type Panda was studied by monitoring the variation of the birefringence during the gluing procedure. The isothermal curing process at 100°C of the epoxy-based adhesive is characterized by the reduction of birefringence during curing. Significant transversal strain is introduced into the fiber during the cool down period, which is due to different thermal expansion coefficients of the silica and the glue. When the slow axis of the HiBi fiber is oriented parallel to the surface, the glue-induced transversal strain reduces the birefringence of the fiber by ΔB = -6.6 10-5 and when it is perpendicular to the surface, it is increased by ΔB = 1.1 10-5. It can be estimated that for conventional FBGs in single mode fibers a glue-induced birefringence in the order of ΔB = 3.4 10-5 can be expected, which has to be taken into account if in surface-mounted FBG-based strain measurements a high accuracy has to be achieved.